Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory

A stochastic orbital approach to the resolution of identity (RI) approximation for 4-index electron repulsion integrals (ERIs) is presented. The stochastic RI-ERIs are then applied to second order Moller–Plesset perturbation theory (MP2) utilizing a multiple stochastic orbital approach. The introduction of multiple stochastic orbitals results in an O(NAO3) scaling for both the stochastic RI-ERIs and stochastic RI-MP2, NAO being the number of basis functions. For a range of water clusters we demonstrate that this method exhibits a small prefactor and observed scalings of O(Ne2.4) for total energies and O(Ne3.1) for forces (Ne being the number of correlated electrons), outperforming MP2 for clusters with as few as 21 water molecules.